Finite Group Databasebeta

← #34060879

Subgroups — #34060879

Order 19072.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750630C211yesmaximal, characteristic
2#23750561C211yesmaximal, characteristic
3#23750495C214yesmaximal
4#23750180C211yesmaximal, characteristic
5C2×#14558746C2212yes—
6C2×C4×#10597010C2212yes—
7#18011978—21no—
8#18011978—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11#18011911C411yescharacteristic, complemented
12#18011902C412yescomplemented
13#18011891—21no—
14#18011887—21no—
15Q8×Dic149—21no—
16#18011876—21no—
17#18011869C2212yes—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558746—24no—
22C2×#11924753—22no—
23C4×#10597010—22no—
24C4×#10597010Q814yescomplemented
25C2×Dic298—21no—
26C2×C4×D149D411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149C2311yescharacteristic
29C4⋊Dic149—22no—
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C412yes—
32#14558715—22no—
33#14558713—22no—
34C4×Dic149—22no—
35C4×Dic149C2×C411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149D411yescharacteristic
38C2×Q8×C149—21no—
39C4⋊C4×C149—21no—
40C4⋊C4×C149C2×C412yes—
41C42×C149C2×C411yescharacteristic
42C2×#10597010—24no—
43C2×#10597010—42no—
44C2×#10597010—42no—
45#11924753—42no—
46C22×D149C2×D411yescharacteristic
47Dic298—42no—
48C2×Dic149—22no—
49C2×Dic149C22⋊C411yescharacteristic
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C2×D411yescharacteristic
52C4×D149—41no—
53C4×D149—41no—
54C4×D149C2×Q812yes—
55C4×D149#4112yes—
56Q8×C149—42no—
57C2×C4×C149—22no—
58C2×C4×C149C22⋊C411yescharacteristic
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22×C411yescharacteristic
61C22×C149C2×C22⋊C411yescharacteristic
62C2×D149—21no—
63C2×D149—21no—
64C2×D149C22⋊Q812yes—
65#10597010—44no—
66C4×C149—21no—
67C4×C149—21no—
68C4×C149—42no—
69C4×C149C4×Q812yes—
70Dic149—21no—
71Dic149—21no—
72Dic149—42no—
73Dic149#12411yescharacteristic
74Dic149C4⋊Q811yescharacteristic
75C2×C149#39111yescharacteristic
76C2×C149#42111yescharacteristic
77C2×C149#42111yescharacteristic
78D149—22no—
79C149#199511yescharacteristic, complemented, Sylow
80#1995—1491nomaximal, Sylow
81#533—1491no—
82#423—1491no—
83#376—1491no—
84#339—1494no—
85C2×M16—1492no—
86C4⋊Q8—1491no—
87C4⋊Q8#1059701011yescharacteristic, complemented
88#125—1492no—
89C22⋊Q8—2981no—
90C22⋊Q8—2981no—
91C4×Q8—2981no—
92C4×Q8—2981no—
93#117—1492no—
94C2×C42—1492no—
95C2×C42—1491no—
96C4⋊C8—2981no—
97C4⋊C8—2981no—
98#95—2981no—
99#95—2981no—
100C2×Q8—21no—
101C2×Q8—2981no—
102C22×C4—2982no—
103C22×C4—1491no—
104C22×C4—1491no—
105C22×C4—1491no—
106M16—2984no—
107C2×C8—2982no—
108C4⋊C4—21no—
109C4⋊C4—2982no—
110C4⋊C4—2982no—
111C4⋊C4—2981no—
112C4⋊C4—1492no—
113C4⋊C4C2×#1059701012yes—
114C22⋊C4—2982no—
115C42—2982no—
116C42—2982no—
117C42—1494no—
118C42—1491no—
119C42—1491no—
120C42—1491no—
121C42C2×#1059701011yescharacteristic
122C23—1491no—
123Q8—42no—
124Q8—5962no—
125C2×C4—22no—
126C2×C4—2984no—
127C2×C4—2982no—
128C2×C4—5961no—
129C2×C4—5961no—
130C2×C4—5962no—
131C2×C4—5962no—
132C2×C4—1491no—
133C2×C4—1491no—
134C2×C4—1491no—
135C2×C4—1492no—
136C2×C4—1492no—
137C2×C4C22⋊#1059701011yescharacteristic
138C2×C4C22⋊#1059701011yescharacteristic
139C2×C4C22×#1059701011yescharacteristic
140C8—5962no—
141C22—2981no—
142C22—2981no—
143C22—1492no—
144C22C2×C22⋊#1059701011yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—2981no—
149C4—2981no—
150C4—5964no—
151C4—5962no—
152C4—1491no—
153C4—1491no—
154C4Q8×#1059701012yes—
155C2—2982no—
156C2(C2×#10597010)⋊Q811yescharacteristic
157C2#2375062311yescharacteristic
158C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1995
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #18011911C4semidirect
12. #18011902C4semidirect
19. C4⋊Q8×C149C4semidirect
24. C4×#10597010Q8semidirect
79. C149#1995semidirect
87. C4⋊Q8#10597010semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237506302
#237505612
#237504952
#237501802
#1995149